Multiply the following complex numbers, marked as blue dots on the graph: $(2 e^{2\pi i / 3}) \cdot (3 e^{\pi i / 2})$ (Your current answer will be plotted in orange.)
Explanation: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $2 e^{2\pi i / 3}$ ) has angle $\frac{2}{3}\pi$ and radius $2$ The second number ( $3 e^{\pi i / 2}$ ) has angle $\frac{1}{2}\pi$ and radius $3$ The radius of the result will be $2 \cdot 3$ , which is $6$ The angle of the result is $\frac{2}{3}\pi + \frac{1}{2}\pi = \frac{7}{6}\pi$ The radius of the result is $6$ and the angle of the result is $\frac{7}{6}\pi$.